MULTIPLICITY ONE FOR THE PAIR (GLn(D);GLn(E))
Let F be a local field of characteristic zero. Let D be a quaternion algebra over F . Let E be a quadratic field extension of F . Let μ be a character of E × . We study the distinction problem for the pair (GL n ( D );GL n ( E )) and we prove that any bi-(GL n ( E ); μ )-equivariant tempered general...
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| Veröffentlicht in: | Transformation groups 2023-06, Vol.28 (2), p.853-866 |
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| creator | LU, HENGFEI |
| description | Let
F
be a local field of characteristic zero. Let
D
be a quaternion algebra over
F
. Let
E
be a quadratic field extension of
F
. Let
μ
be a character of
E
×
. We study the distinction problem for the pair (GL
n
(
D
);GL
n
(
E
)) and we prove that any bi-(GL
n
(
E
);
μ
)-equivariant tempered generalized function on GL
n
(
D
) is invariant with respect to an anti-involution. Then it implies that dimHom
GL
n
(
E
)
(π;
μ
) ≤ 1 by the generalized Gelfand-Kazhdan criterion. Thus we give a new proof to the fact that (GL
2
n
(
F
);GL
n
(
E
)) is a Gelfand pair when
μ
is trivial and
D
splits. |
| doi_str_mv | 10.1007/s00031-022-09713-z |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_2811673231</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2811673231</sourcerecordid><originalsourceid>FETCH-LOGICAL-c200t-499d4a18ffc8860847fd966441dd78e3bb2aaa42ffee40cece97aa8ec890a5073</originalsourceid><addsrcrecordid>eNp9kE9LAzEUxIMoWKtfwNOCl_YQffnTJIunUrftwuqWsgU9hXQ3EYu2NWkP9tObuoI3TzM8ZubBD6FrArcEQN4FAGAEA6UYUkkYPpygDhnE00CJ59PoQTHMmaDn6CKEFQCRQogOwo-LospnRT7Kq5ekfMqScTlPqmmWzIb5POlNinXvoX9_lKzfv0RnzrwHe_WrXbQYZ9Voiotyko-GBa4pwA7zNG24Icq5WikBikvXpEJwTppGKsuWS2qM4dQ5aznUtrapNEbZWqVgBiBZF920u1u_-dzbsNOrzd6v40tNFSFCMspITNE2VftNCN46vfVvH8Z_aQL6iEW3WHTEon-w6EMssbYUYnj9av3f9D-tb_u5YD8</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2811673231</pqid></control><display><type>article</type><title>MULTIPLICITY ONE FOR THE PAIR (GLn(D);GLn(E))</title><source>SpringerLink Journals - AutoHoldings</source><creator>LU, HENGFEI</creator><creatorcontrib>LU, HENGFEI</creatorcontrib><description>Let
F
be a local field of characteristic zero. Let
D
be a quaternion algebra over
F
. Let
E
be a quadratic field extension of
F
. Let
μ
be a character of
E
×
. We study the distinction problem for the pair (GL
n
(
D
);GL
n
(
E
)) and we prove that any bi-(GL
n
(
E
);
μ
)-equivariant tempered generalized function on GL
n
(
D
) is invariant with respect to an anti-involution. Then it implies that dimHom
GL
n
(
E
)
(π;
μ
) ≤ 1 by the generalized Gelfand-Kazhdan criterion. Thus we give a new proof to the fact that (GL
2
n
(
F
);GL
n
(
E
)) is a Gelfand pair when
μ
is trivial and
D
splits.</description><identifier>ISSN: 1083-4362</identifier><identifier>EISSN: 1531-586X</identifier><identifier>DOI: 10.1007/s00031-022-09713-z</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Fields (mathematics) ; Lie Groups ; Mathematics ; Mathematics and Statistics ; Number theory ; Quaternions ; Topological Groups</subject><ispartof>Transformation groups, 2023-06, Vol.28 (2), p.853-866</ispartof><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022</rights><rights>The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c200t-499d4a18ffc8860847fd966441dd78e3bb2aaa42ffee40cece97aa8ec890a5073</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00031-022-09713-z$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00031-022-09713-z$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>LU, HENGFEI</creatorcontrib><title>MULTIPLICITY ONE FOR THE PAIR (GLn(D);GLn(E))</title><title>Transformation groups</title><addtitle>Transformation Groups</addtitle><description>Let
F
be a local field of characteristic zero. Let
D
be a quaternion algebra over
F
. Let
E
be a quadratic field extension of
F
. Let
μ
be a character of
E
×
. We study the distinction problem for the pair (GL
n
(
D
);GL
n
(
E
)) and we prove that any bi-(GL
n
(
E
);
μ
)-equivariant tempered generalized function on GL
n
(
D
) is invariant with respect to an anti-involution. Then it implies that dimHom
GL
n
(
E
)
(π;
μ
) ≤ 1 by the generalized Gelfand-Kazhdan criterion. Thus we give a new proof to the fact that (GL
2
n
(
F
);GL
n
(
E
)) is a Gelfand pair when
μ
is trivial and
D
splits.</description><subject>Algebra</subject><subject>Fields (mathematics)</subject><subject>Lie Groups</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Number theory</subject><subject>Quaternions</subject><subject>Topological Groups</subject><issn>1083-4362</issn><issn>1531-586X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><recordid>eNp9kE9LAzEUxIMoWKtfwNOCl_YQffnTJIunUrftwuqWsgU9hXQ3EYu2NWkP9tObuoI3TzM8ZubBD6FrArcEQN4FAGAEA6UYUkkYPpygDhnE00CJ59PoQTHMmaDn6CKEFQCRQogOwo-LospnRT7Kq5ekfMqScTlPqmmWzIb5POlNinXvoX9_lKzfv0RnzrwHe_WrXbQYZ9Voiotyko-GBa4pwA7zNG24Icq5WikBikvXpEJwTppGKsuWS2qM4dQ5aznUtrapNEbZWqVgBiBZF920u1u_-dzbsNOrzd6v40tNFSFCMspITNE2VftNCN46vfVvH8Z_aQL6iEW3WHTEon-w6EMssbYUYnj9av3f9D-tb_u5YD8</recordid><startdate>20230601</startdate><enddate>20230601</enddate><creator>LU, HENGFEI</creator><general>Springer US</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20230601</creationdate><title>MULTIPLICITY ONE FOR THE PAIR (GLn(D);GLn(E))</title><author>LU, HENGFEI</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c200t-499d4a18ffc8860847fd966441dd78e3bb2aaa42ffee40cece97aa8ec890a5073</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2023</creationdate><topic>Algebra</topic><topic>Fields (mathematics)</topic><topic>Lie Groups</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Number theory</topic><topic>Quaternions</topic><topic>Topological Groups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>LU, HENGFEI</creatorcontrib><collection>CrossRef</collection><jtitle>Transformation groups</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>LU, HENGFEI</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>MULTIPLICITY ONE FOR THE PAIR (GLn(D);GLn(E))</atitle><jtitle>Transformation groups</jtitle><stitle>Transformation Groups</stitle><date>2023-06-01</date><risdate>2023</risdate><volume>28</volume><issue>2</issue><spage>853</spage><epage>866</epage><pages>853-866</pages><issn>1083-4362</issn><eissn>1531-586X</eissn><abstract>Let
F
be a local field of characteristic zero. Let
D
be a quaternion algebra over
F
. Let
E
be a quadratic field extension of
F
. Let
μ
be a character of
E
×
. We study the distinction problem for the pair (GL
n
(
D
);GL
n
(
E
)) and we prove that any bi-(GL
n
(
E
);
μ
)-equivariant tempered generalized function on GL
n
(
D
) is invariant with respect to an anti-involution. Then it implies that dimHom
GL
n
(
E
)
(π;
μ
) ≤ 1 by the generalized Gelfand-Kazhdan criterion. Thus we give a new proof to the fact that (GL
2
n
(
F
);GL
n
(
E
)) is a Gelfand pair when
μ
is trivial and
D
splits.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00031-022-09713-z</doi><tpages>14</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1083-4362 |
| ispartof | Transformation groups, 2023-06, Vol.28 (2), p.853-866 |
| issn | 1083-4362 1531-586X |
| language | eng |
| recordid | cdi_proquest_journals_2811673231 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebra Fields (mathematics) Lie Groups Mathematics Mathematics and Statistics Number theory Quaternions Topological Groups |
| title | MULTIPLICITY ONE FOR THE PAIR (GLn(D);GLn(E)) |
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